1. Field of the Invention
The present invention relates to a two-dimensional photonic crystal surface-emitting laser.
2. Description of the Related Art
Photonic crystals are periodic optical structures formed by arranging a medium having a refractive index different from a refractive index of, for example, semiconductor, with a period on the order of wavelength of light, and applications thereof to various optical devices are being studied.
Examples of the optical devices using the photonic crystals include a two-dimensional photonic crystal surface-emitting laser. Conventional two-dimensional photonic crystal surface-emitting lasers are disclosed in, for example, Japanese Patent Application Laid-open No. 2000-332351, Japanese Patent Application Laid-open No. 2003-23193, and Japanese Patent Application Laid-open No. 2004-296538. For example, FIG. 11 is an exploded perspective view of a two-dimensional photonic crystal surface-emitting laser 100′ disclosed in Japanese Patent Application Laid-open No. 2000-332351. The two-dimensional photonic crystal surface-emitting laser 100′ includes a confinement layer 102′, a lower cladding layer 103′, an active layer 104′, and an upper cladding layer 105′ grown in that order on a substrate 101′. The confinement layer 102′ is formed of n-InP semiconductor and contains air holes 108′ formed in a square-lattice pattern arrayed at a predetermined two-dimensional period. Thus, the air holes 108′ form a photonic crystal in which air medium having a refractive index different from that of the n-InP semiconductor is arrayed periodically. The active layer 104′ has a multiple-quantum well (MQW) structure using GaInAsP semiconductor material and emits a light when a carrier is injected into the active layer 104′. The lower cladding layer 103′ is formed of n-InP semiconductor and the like. The upper cladding layer 105′ is formed of p-InP semiconductor. The lower cladding layer 103′ and the upper cladding layer 105′ sandwich the active layer 104′, and thereby a double heterojunction is formed to confine the carrier. Thus, the carrier that contributes to light emission is confined in the active layer 104′. In this state, an electrode 106′ made of Au is formed on a top surface of the upper cladding layer 105′ and an electrode 107′ made of Au is formed on a bottom surface of the substrate 101′.
When a voltage is applied between the electrodes 106′ and 107′, the active layer 104′ emits a light, so that a light spreading as an evanescent wave from the active layer 104′ is distributed in the two-dimensional photonic crystal formed in the confinement layer 102′. The two-dimensional photonic crystal has a two-dimensional distributed feedback effect. Therefore, similar to a distributed-feedback laser using a typical one-dimensional grating, laser oscillation occurs with the two-dimensional photonic crystal. Furthermore, the distributed-feedback effect of the two-dimensional photonic crystal occurs two dimensionally, so that a coherent single-mode oscillation occurs over a large area of the two-dimensional plane. As a result, surface emission occurs with a single-mode laser light. Principles of the two-dimensional distributed feedback and the surface emission of the two-dimensional photonic crystal surface-emitting laser 100′ are described below in relation to a wave number space of the two-dimensional photonic crystal.
A light that can distributed feedback-operate in the two-dimensional square-lattice photonic crystal operates at X-point, M-point, and Γ-point among symmetric points in a reciprocal lattice space (wave number space) of the photonic crystal. The Γ-point is a point at which a wave number vector k is represented by k=pb1+qb2, where p and q are arbitrary integers and b1 and b2 are reciprocal primitive vectors with minimum magnitudes in a square-lattice. The reciprocal primitive vectors b1 and b2 are perpendicular to each other and their magnitudes are 2π/a where “a” is a lattice constant of the photonic crystal. Similarly, the X-point is a point at which a wave number vector k is represented by either k=(p+(½))b1+qb2 or k=pb1+(q+(½))b2. The M-point is a point at which a wave number vector k is represented by k=(p+(½))b1+(q+(½))b2.
On the other hand, a light that can distributed feedback-operate in the two-dimensional triangular-lattice photonic crystal operates at M-point, K-point, and Γ-point among symmetric points in a wave number space of the photonic crystal. The Γ-point is a point at which a wave number vector k is represented by k=pb1+qb2, where p and q are arbitrary integers and b1 and b2 are reciprocal primitive vectors with minimum magnitudes in a triangular-lattice. In this case, the reciprocal primitive vector b1 and b2 make an angle of 60 degrees therebetween, and their magnitudes are 4π/(√3a) where “a” is a lattice constant of the photonic crystal. Similarly, the M-point is a point at which a wave number vector k is represented by one of k=(p+(½))b1+qb1, k=pb1+(q+(½))b2 and k=(p−(½))b1+(q+(½))b2. The K-point is a point at which a wave number vector k is represented by either k=(p+(⅓))b1+(q+(⅓))b2 or k=(p−(⅓))b1+(q+(⅔))b2.
The two-dimensional photonic crystal surface-emitting lasers disclosed in Japanese Patent Application Laid-open No. 2000-332351 employs the Γ-point of either the two-dimensional square-lattice photonic crystal or the two-dimensional triangular-lattice photonic crystal as an operating point of two-dimensional distributed feedback.
A principle of the two-dimensional distributed feedback is described in relation to diffraction of a light by a photonic crystal lattice. The diffraction of a light in a periodic structure such as a crystal lattice means that a light with a wave number vector k changes to a light with a wave number vector of k′=k+p′b1+q′b2, where p′ and q′ are arbitrary integers and b1 and b2 are reciprocal primitive vectors. Assuming that a light with a wave number vector k=pb1+qb2, that is, a light at the Γ-point, is diffracted such that p′=−2p and q′=−2q are satisfied, a light after diffraction has a wave number vector k′=−k. That is, the light at the Γ-point is coupled with a wave that travels in a direction opposite to a direction of a light before diffraction. Because lights that travel in opposite directions are coupled with each other, distributed feedback occurs. When a light is diffracted such that p′=−p+q and q′=−q−p are satisfied, a wave number vector of a diffracted light is represented by k′=qb1−pb2. In this state, the light is coupled with a wave tilted by 90 degrees from a light before diffraction in the case of a square-lattice, and with a wave tilted by 120 degrees from a light before diffraction in the case of a triangular-lattice. Furthermore, when a light is diffracted such that p′=−p−q and q′=−q+p are satisfied, a wave number vector of a diffracted light is represented by k′=−qb1+pb2. In this state, the light is coupled with a wave tilted by −90 degrees from a light before diffraction in the case of a square-lattice, and with a wave tilted by −120 degrees from a light before diffraction in the case of a triangular-lattice. Thus, the light at the Γ-point is fed back to an original position, being diffracted at an arbitrary position on a crystal lattice and coupled with a wave that travels in the abovementioned predetermined direction. That is, the two-dimensional distributed feedback occurs with the light at the Γ-point.
A principle of the surface emission is also described in relation to diffraction of a light. When a light at the Γ-point is diffracted such that p′=−p and q′=−q are satisfied, k′=0 is obtained. The fact that a wave number vector k′ in a two-dimensional in-plane is zero (k′=0) means that the light travels in a direction normal to a plane of a photonic crystal. That is, the light at the Γ-point has such property that surface emission occurs due to an effect of grating couple, with which the light is diffracted and travels in a direction normal to the plane of the photonic crystal. As a result, the light at the Γ-point distributed-feedbacks two-dimensionally, and surface-emits as well.
As described above, the two-dimensional photonic crystal surface-emitting laser causes surface emission with a light at the Γ-point in a wave number space of the photonic crystal formed on the confinement layer. The surface emission is achieved as a coherent single-mode laser light over a large area of a two-dimensional plane.
However, in the conventional two-dimensional photonic crystal surface-emitting lasers, if a two-dimensional distributed feedback effect of the photonic crystal structure is optimized to improve the in-plane optical confinement, the intensity of the surface emission decreases. On the other hand, if the surface emitting property of the photonic crystal structure is optimized to increase the intensity of the surface emission, the in-plane optical confinement degrades. Thus, the two-dimensional distributed feedback effect and the surface emitting property cannot independently be optimized.